1. Unit Conversion and Dimensional Analysis Notes
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2. Units of Measurements Temperature Density K = °C + 273 mass Density =
Quantity
Base Unit
Symbol
Length
meter m
Mass
gram g
Volume
liter L
Temperature
Kelvin or Celsius
K or °C
Time
seconds s
Energy
joules or calories
J or cal
Density
grams per cubic centimeter
g/cm3
Temperature
Density
K = °C + 273
°C = K – 273
mass
volume
Density =

3. Volume can be measured by the length, width and height of an object:
Units of Volume
Volume can be measured by the length, width and height of an object:
Volume (cm3) = Length x width x height
2 main units for volume: mL and cm3
conversion factor  1 mL = 1 cm3
Units of Energy
1 J = cal
1 cal = J
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4. Commonly Used Metric Prefixes
The table below lists the prefixes in common use.
Commonly Used Metric Prefixes
Prefix
Symbol
Meaning
Factor
mega M
1 million times larger than the unit it precedes
106
kilo k
1000 times larger than the unit it precedes
103
deci d
10 times smaller than the unit it precedes
10-1
centi c
100 times smaller than the unit it precedes
10-2
milli m
1000 times smaller than the unit it precedes
10-3
micro μ
1 million times smaller than the unit it precedes
10-6
nano n
1 billion times smaller than the unit it precedes
10-9
pico p
1 trillion times smaller than the unit it precedes
10-12
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5. UNIT CONVERSION How can you convert U.S. dollars to euros?
CHEMISTRY & YOU
UNIT CONVERSION
How can you convert U.S. dollars to euros?
Because each country’s currency compares differently with the U.S. dollar, knowing how to convert currency units correctly is essential. Conversion problems are readily solved by a problem-solving approach called dimensional analysis.
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6. 1 dollar = 4 quarters = 10 dimes = 20 nickels = 100 pennies
Conversion Factors
Conversion Factors
For example:
1 dollar = 4 quarters = 10 dimes = 20 nickels = 100 pennies
1 meter = 10 decimeters = 100 centimeters = 1000 millimeters
1 m =
100 cm 1 or
If you think about any number of everyday situations, you will realize that a quantity can usually be expressed in several different ways.
These are all expressions, or measurements, of the same amount of money.
The same thing is true of scientific quantities. These are different ways to express the same length.
Whenever two measurements are equivalent, a ratio of the two measurements will equal 1, or unity.
For example, you can divide both sides of the equation 1 m = 100 cm by 1 m or by 100 cm.
The measurement in the numerator (on the top) is equivalent to the measurement in the denominator (on the bottom).
The conversion factors shown below are read “one hundred centimeters per meter” and “one meter per hundred centimeters.”
conversion factors
A conversion factor is a ratio of equivalent measurements.

7. m 100 Conversion Factors 1 cm
1 meter
100 centimeters
Larger unit
Smaller unit
100 1 m cm
Smaller number
Larger number
Conversion factors are useful in solving problems in which a given measurement must be expressed in some other unit of measure.
The figure above illustrates another way to look at the relationships in a conversion factor.
The smaller number is part of the measurement with the larger unit.
The larger number is part of the measurement with the smaller unit.
Conversion factors do not affect the number of significant figure and rounding of a calculated answer.
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8. Dimensional Analysis
Dimensional Analysis
Dimensional analysis is a way to analyze and solve problems using the units, or dimensions, of the measurements.
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9. Using Dimensional Analysis Examples
Sample Problem 3.9
Using Dimensional Analysis Examples
Follow along with your practice worksheet.
1. How many seconds are in a workday that lasts exactly eight hours?
Analyze List the knowns and the unknown. 1
UNKNOWN
seconds worked = ? s
KNOWN
Time worked = 8 h
1 hour = 60 min
1 min = 60 s
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10. 2 Calculate Solve for the unknown. 60 min 28,800 s 1 8 h 60 s = =
Sample Problem 3.9
Calculate Solve for the unknown. 2
Draw a T table.
Start with the given measurement in the top left box.
Determine the first conversion factor. Place the unwanted unit in the next bottom box (denominator) to cancel the unit. Place the desired unit in the next top box.
Determine next conversion factor until units cancel each other out, leaving the desired unit.
Multiply the top numbers (numerator) together. Multiply the bottom numbers (denominator) together. Then divide. Write answer in correct # SigFigs & Scientific Notation.
To convert time in hours to time in seconds, you’ll need two conversion factors. First you must convert hours to minutes: h  min. Then you must convert minutes to seconds: min  s. Identify the proper conversion factors based on the relationships 1 h = 60 min and 1 min = 60 s.
The first conversion factor is based on 1 h = 60 min. The unit hours must be in the denominator so that the known unit will cancel.
The second conversion factor is based on 1 min = 60 s. The unit minutes must be in the denominator so that the desired units (seconds) will be in your answer.
Before you do the actual arithmetic, it’s a good idea to make sure that the units cancel and that the numerator and denominator of each conversion factor are equal to each other.
60 min
28,800 s 1
8 h
60 s = =
x 104 s
1 min
1 h

11. Converting Between Metric Units (Number 2 on your worksheet)
Sample Problem 3.11
Converting Between Metric Units
(Number 2 on your worksheet)
2. Express 750 dg in grams.
(Refer to your quick references on p.6 of your notebook if you need to refresh your memory of metric prefixes.)
In chemistry, as in everyday life, you often need to express a measurement in a unit different from the one given or measured initially.
Dimensional analysis is a powerful tool for solving conversion problems in which a measurement with one unit is changed to an equivalent measurement with another unit.
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12. Sample Problem 3.11
Analyze List the knowns and the unknown. 1
UNKNOWN
Mass = ? g
KNOWN
Mass = 750 dg
1 g = 10 dg
Calculate Solve for the unknown. 2
750 dg
1 g
750 g 10 =
= 75 g
The desired conversion is decigrams  grams. Multiply the given mass by the proper conversion factor.
10 dg
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13. Using Density as a Conversion Factor (Number 3 on your worksheet)
Sample Problem 3.12
Using Density as a Conversion Factor
(Number 3 on your worksheet)
What is the volume of a pure silver coin that has a mass of 14 g? The density of silver (Ag) is 10.5 g/cm3.
Density can be used to write two conversion factors. To figure out which one you need, consider the units of your given quantity and the units needed in your answer.
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14. 1 2 14 cm3 Ag 10.5 14 g Ag 1 cm3 Ag = = 1.3 cm3 Ag 10.5 g Ag
Sample Problem 3.12
Analyze List the knowns and the unknown. 1
UNKNOWN
Volume = ? cm3
KNOWN
Mass = 14 g
Density of silver = 10.5 g/cm3
 10.5 g = 1 cm3
Calculate Solve for the unknown. 2
14 cm3 Ag
10.5
14 g Ag
You need to convert the mass of the coin into a corresponding volume. The density gives you the following relationship between volume and mass: 1 cm3 Ag = 10.5 g Ag. Multiply the given mass by the proper conversion factor to yield an answer in cm3.
1 cm3 Ag =
= 1.3 cm3 Ag
10.5 g Ag
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15. Dimensional Analysis
Multistep Problems
Many complex tasks in your life are best handled by breaking them down into smaller, manageable parts.
Similarly, many complex word problems are more easily solved by breaking the solution down into steps.
When converting between units, it is often necessary to use more than one conversion factor.
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16. Converting Between Metric Units (Number 4 and 5 on your worksheet)
Sample Problem 3.13
Converting Between Metric Units
(Number 4 and 5 on your worksheet)
The diameter of a sewing needle is cm. What is the diameter in micrometers?
The density of manganese (Mn), a metal, is 7.21 g/cm3. What is the density of manganese expressed in units of kg/m3?
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17. Sample Problem 3.13
Analyze List the knowns and the unknown. 1
UNKNOWN length = ? μm
KNOWNS length = cm = 7.3 x 10-2 cm 102 cm = 1 m 1 m = 106 μm
Calculate Solve for the unknown. 2
7.3 x 104 μm
7.3 x 10-2 cm
1 m
106 μm =
102 cm
1 m
102
The desired conversion is centimeters  micrometers. The problem can be solved in a two-step conversion. First change centimeters to meters; then change meters to micrometers: centimeters  meters  micrometers.
= 7.3 x 102 μm
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18. 1 2 Analyze List the knowns and the unknown.
Sample Problem 3.14
Analyze List the knowns and the unknown. 1
UNKNOWN density of Mn = ? kg/m3
KNOWNS density of Mn = 7.21 g/cm3 103 g = 1 kg 106 cm3 = 1m3
Calculate Solve for the unknown. 2
7.21 x 106 kg
7.21 g
1 kg
106 cm3 =
The desired conversion is g/cm3  kg/m3. The mass unit in the numerator must be changed from grams to kilograms: g  kg. In the denominator, the volume unit must be changed from cubic centimeters to cubic meters: cm3  m3. Note that the relationship 106 cm3 = 1 m3 was derived by cubing the relationship 102 cm = 1 m. That is, (102 cm)3 = (1m)3, or 106 cm3 = 1 m3.
1 cm3
103 g
1 m3
103 m3
= 7.21 x 103 kg/m3
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